We present the first measurements of Charons far-ultraviolet surface reflectance, obtained by the Alice spectrograph on New Horizons. We find no measurable flux shortward of 1650 A, and Charons geometric albedo is $<0.019$ ($3sigma$) at 1600 A. From 1650--1725 A Charons geometric albedo increases to $0.166pm0.068$, and remains nearly constant until 1850 A. As this spectral shape is characteristic of H$_2$O ice absorption, Charon is the first Kuiper belt object with a H$_2$O ice surface to be detected in the far-ultraviolet. Charons geometric albedo is $sim3.7$ times lower than Enceladus at these wavelengths, but has a very similar spectral shape. We attribute this to similarities in their surface compositions, and the difference in absolute reflectivity to a high concentration or more-absorbing contaminants on Charons surface. Finally, we find that Charon has different solar phase behavior in the FUV than Enceladus, Mimas, Tethys, and Dione, with a stronger opposition surge than Enceladus and a shallower decline at intermediate solar phase angles than any of these Saturnian satellites.